Rabbi Shim'on ben Pazi noted a contradiction: [B'reshis 1:16] says, "God made the two big luminaries" and "the big luminary… and the small luminary".

The moon said to God: "Master of the world, is it possible for two kings to use one crown?"

He told her: "Go diminish yourself."

She told him: "Master of the world, because I said something proper to you I have to diminish myself?"

He told her: "Go and rule [=shine] by day and night."

(And the conversation continued further.)

Presumably this midrash is not meant literally. (Moons don't talk, for one thing.) But my question will assume it's literal. In other words, my question will be about the storyline of the midrash, assuming its premise.

My question is: In what sense was the moon diminished? Here are the two most reasonable possibilities I can see:

The sun and moon were the same size (say, a million kilometers' diameter, like the sun is now), and the moon shrank to the 3500 kilometers' diameter it is now.

The sun and moon were the same apparent size as viewed from earth (same angular diameter) — as they are in fact now! — and the moon shrank in the sense that now it wanes.

Keep in mind that the midrash's premise may have included the idea that the Sun and Moon are both two-dimensional light sources rather than three-dimensional, massive bodies at varying distances from the Earth.
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Isaac MosesFeb 24 '12 at 18:19

7 Answers
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I think I remember learning in elementary school that the Moon and the Sun had, as they have now, the same angular diameter when viewed from the Earth, and they also had coronas of equal size, so their total sizes, including coronas, were equal. When the Moon complained about their equality, literally in terms of a "crown" (which a corona resembles and which "corona" literally means), God diminished it by removing its corona.

The explanation referenced in my answer here (I'm still looking for the underlying source - it must be in some maamar or sicha) seems to indicate that the "diminishment" is closer to your second possibility - though focusing not so much on the moon's waxing and waning, but on the fact that it is not self-luminous but receives its light from the sun. (Is there any possible arrangement - perhaps if the moon wasn't tidally locked to earth - in which it could be reflective but not wax and wane, like the planets?)

The Moon would have to remain outside the space between the Earth and the Sun if it were to not wax and wane. The planets that are sometimes inside that space - Mercury and Venus - "appear to go through phases like the Moon.", because we sometimes see part or all of the side of them that is not facing the Sun. This would be possible (geometrically - I have no idea about whether such an orbit is physically possible) if the Moon revolved about the Earth at exactly the same rate that the Earth revolves about the Sun.
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Isaac MosesFeb 24 '12 at 20:08

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Yes, if the moon were at the L2 Lagrange point, it would always be full, while if it were at L1, it would always be new. While it is impossible to remain exactly at these points, since they are dynamically unstable, we have put satellites around L2 in special "halo orbits" that are relatively stable.
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JeremyFeb 24 '12 at 20:26

see my answer. The sources on page 218 of Likutei Sichos vol 32 may be a good place to look as well - hebrewbooks.org/….
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MenachemJun 5 '12 at 23:01

The moon, when she was first created, was a glistening jewel. She did not merely reflect light, but rather transformed it and brought out its inner beauty, much as a precious stone glistens with a secret, hidden light all its own. In her own way, the moon was greater than the sun -- for the sun only shines from its surface, whereas the moon shone from its inner essence. The sun holds the light that extends outward, whereas the moon holds the light of being.

And so will be, once again, and much more so, in the time to come, once we have transformed the world with the Torah and its mitzvahs. (R. Isaac of Homil, Shnei Me'orot)

Rabbeinu Bechayei, in his commentary on Bamidbar 28:15 (relevant part starts middle of second column), says that the sun and moon were created the same size they are now. The lessening of the moon refers to the lessening of light. Originally they were created giving off equal light, but the moon was subsequently dimmed.

And now I see that the Tosefes B'racha (by the author of the Tora T'mima) to Bamidbar 28:15 also, like Rabenu Bachye (or however it's to be transliterated), says the moon diminished in luminosity. (He offers no evidence.)
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msh210♦Jul 20 '12 at 3:19

I would say its luminosity diminished. For most heavenly bodies, the angular size is too small to be resolved by the eye, but the brightness varies by orders of magnitude, so when we say some object is greater or lesser than another, we almost always mean luminosity.

As another option, recall that the Moon was created by a collision of a Mars-sized object with the Earth about 4 Gyr ago. That would be a dimunition in size by a factor of 2 in diameter, and almost 10 in mass.

When the moon was first formed it was much closer to Earth. Over the past 4.5 billion years the moon has been slowly drifting further away, and as a result it would have first appeared 15x larger in the sky than it does today.

This is of course subject to interpretation. Elsewhere, we see that Chazal subscribed to the scientific belief of the Sun moving in front of the rakia. So offhand, I don't see the possibility of a more distant Sun, such that we are speaking of apparent size.

To properly answer this question, I think an investigation is in order into the contemporary scientific beliefs regarding the relative sizes of sun and moon in the time of Chazal, as well as the Babylonian model which Chazal seem to have adopted. So what I wrote is quite possibly wrong, but is, I think, the proper way to go about answering this question.